Quantum Topology Seminar
Dr. Yuting Hu
Southern University of Science and Technology
Magnetic-Electric duality in 2D topological phases
Abstract: In this talk, I will present an Electric-Magnetic duality in 2D topological phases. We use the twisted quantum double model (also known as Dijkgraaf-Witten theory), which is a discrete topological quantum field theory arising from the category $Vect^\alpha_G$ of graded vector spaces, where $G$ is a finite group and $\alpha \in H^3(G, U(1))$. We prove that every Morita equivalence between two such categories, say, $Vect^\alpha_G$ and $Vect^{\alpha'}_{G'}$, is induced by an isomorphism between the corresponding twisted quantum doubles $D^\alpha(G)$ and $D^{\alpha'}(G')$, which we explicitly construct via a Fourier transform. Then we apply this isomorphism to define an electric-magnetic duality in the twisted quantum double models.
Thursday September 17, 2020 at 4:00 PM in Zoom